The only other way I've thought of so far is pretty hacky… I was thinking of trying to hide the original category titles and replacing each one manually with CSS using using body class tags to target each category page separately—but I don't think it's an elegant solution and it wouldn't be easy to do if you had a ton of categories.

That did the trick, thank you so much! It's not ideal to remove the category header all together, but this site shouldn't get too complex and will work for now. Maybe I will try to create some custom menu in the future. Thanks again for all of your responses & help!

@designsimply (2): What I thought of is create a mask in front of "Category archives: ", and move the whole archive header to the left (in which case I also need a replacement bg). Here it is (values based on the default version of the theme, not on beks323's customization):

@justpi (2): that's tricky! Maybe too tricky! The mask part didn't work for me in a test but I think it's close. After mulling it over, I think deleting the whole thing is the way to go and your first example with the specific category page selectors is the next best route if someone insists on updating category page titles with CSS in Twenty Thirteen.

It was good to look into this. I did also ask about changing how the category labels work in Twenty Thirteen, but it was designed as is for a reason and is meant to be blog-focused where the extra "Category Archives:" label makes sense. Hopefully the option to hide it all together will work for anyone who wants to change it.